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sfad_example.cpp
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31 
32 // sfad_example
33 //
34 // usage:
35 // sfad_example
36 //
37 // output:
38 // prints the results of differentiating a simple function with forward
39 // mode AD using the Sacado::Fad::SFad class (uses static memory allocation
40 // for the number of derivative components, meaning this must be known
41 // at compile time.
42 
43 #include <iostream>
44 #include <iomanip>
45 
46 #include "Sacado.hpp"
47 
48 // The function to differentiate
49 template <typename ScalarT>
50 ScalarT func(const ScalarT& a, const ScalarT& b, const ScalarT& c) {
51  ScalarT r = c*std::log(b+1.)/std::sin(a);
52 
53  return r;
54 }
55 
56 // The analytic derivative of func(a,b,c) with respect to a and b
57 void func_deriv(double a, double b, double c, double& drda, double& drdb)
58 {
59  drda = -(c*std::log(b+1.)/std::pow(std::sin(a),2.))*std::cos(a);
60  drdb = c / ((b+1.)*std::sin(a));
61 }
62 
63 int main(int argc, char **argv)
64 {
65  double pi = std::atan(1.0)*4.0;
66 
67  // Values of function arguments
68  double a = pi/4;
69  double b = 2.0;
70  double c = 3.0;
71 
72  // Number of independent variables
73  int num_deriv = 2; // Must be == 2 (see below)
74 
75  // Fad objects
76  Sacado::Fad::SFad<double,2> afad(num_deriv, 0, a); // First (0) indep. var
77  Sacado::Fad::SFad<double,2> bfad(num_deriv, 1, b); // Second (1) indep. var
78  Sacado::Fad::SFad<double,2> cfad(c); // Passive variable
79  Sacado::Fad::SFad<double,2> rfad; // Result
80 
81  // Compute function
82  double r = func(a, b, c);
83 
84  // Compute derivative analytically
85  double drda, drdb;
86  func_deriv(a, b, c, drda, drdb);
87 
88  // Compute function and derivative with AD
89  rfad = func(afad, bfad, cfad);
90 
91  // Extract value and derivatives
92  double r_ad = rfad.val(); // r
93  double drda_ad = rfad.dx(0); // dr/da
94  double drdb_ad = rfad.dx(1); // dr/db
95 
96  // Print the results
97  int p = 4;
98  int w = p+7;
99  std::cout.setf(std::ios::scientific);
100  std::cout.precision(p);
101  std::cout << " r = " << r << " (original) == " << std::setw(w) << r_ad
102  << " (AD) Error = " << std::setw(w) << r - r_ad << std::endl
103  << "dr/da = " << std::setw(w) << drda << " (analytic) == "
104  << std::setw(w) << drda_ad << " (AD) Error = " << std::setw(w)
105  << drda - drda_ad << std::endl
106  << "dr/db = " << std::setw(w) << drdb << " (analytic) == "
107  << std::setw(w) << drdb_ad << " (AD) Error = " << std::setw(w)
108  << drdb - drdb_ad << std::endl;
109 
110  double tol = 1.0e-14;
111  if (std::fabs(r - r_ad) < tol &&
112  std::fabs(drda - drda_ad) < tol &&
113  std::fabs(drdb - drdb_ad) < tol) {
114  std::cout << "\nExample passed!" << std::endl;
115  return 0;
116  }
117  else {
118  std::cout <<"\nSomething is wrong, example failed!" << std::endl;
119  return 1;
120  }
121 }
atan(expr.val())
KOKKOS_INLINE_FUNCTION mpl::enable_if_c< ExprLevel< Expr< T1 > >::value==ExprLevel< Expr< T2 > >::value, Expr< PowerOp< Expr< T1 >, Expr< T2 > > > >::type pow(const Expr< T1 > &expr1, const Expr< T2 > &expr2)
expr expr1 expr1 expr1 c expr2 expr1 expr2 expr1 expr2 expr1 expr1 expr1 expr1 c expr2 expr1 expr2 expr1 expr2 expr1 expr1 expr1 expr1 c *expr2 expr1 expr2 expr1 expr2 expr1 expr1 expr1 expr1 c expr2 expr1 expr2 expr1 expr2 expr1 expr1 expr1 expr2 expr1 expr2 expr1 expr1 expr1 expr2 expr1 expr2 expr1 expr1 expr1 c
int main()
Definition: ad_example.cpp:191
void func_deriv(double a, double b, double c, double &drda, double &drdb)
sin(expr.val())
log(expr.val())
const double tol
const T func(int n, T *x)
Definition: ad_example.cpp:49
fabs(expr.val())
cos(expr.val())